Compound mold and structured surface articles containing geometric structures with compound faces and method of making same

ABSTRACT

A structured surface articles such as molds or sheeting are formed on a compound substrate including a machined substrate and a replicated substrate. In one embodiment, the structured surface is a cube corner element on a compound substrate. In another embodiment, the structured surface is a geometric structure that has a plurality of faces, where one face is located on the machined substrate and another face is located on the replicated substrate. In yet another embodiment, at least some of the faces include a compound face with a portion formed on the machined substrate and a portion formed on the replicated substrate. The method of making a structured surface article including a geometric structure having a plurality of faces includes forming an array of geometric structures in a first surface of a machined substrate; passivating selected locations of the first surface of the machined substrate; forming a replicated substrate of the machined substrate to form a compound substrate; forming an array of second geometric structures on a second surface opposite the first surface on the machined substrate; and removing selected portions from the second surface of the machined substrate.

BACKGROUND

The present invention relates generally to structured surfacesfabricated using microreplication techniques. The invention hasparticular application to structured surfaces that compriseretroreflective cube corner elements.

The reader is directed to the glossary at the end of the specificationfor guidance on the meaning of certain terms used herein.

It is known to use microreplicated structured surfaces in a variety ofend use applications such as retroreflective sheeting, mechanicalfasteners, and abrasive products. Although the description that followsfocuses on the field of retroreflection, it will be apparent that thedisclosed methods and articles can equally well be applied to otherfields that make use of microreplicated structured surfaces.

Cube corner retroreflective sheeting typically comprises a thintransparent layer having a substantially planar front surface and a rearstructured surface comprising a plurality of geometric structures, someor all of which include three reflective faces configured as a cubecorner element.

Cube corner retroreflective sheeting is commonly produced by firstmanufacturing a master mold that has a structured surface, suchstructured surface corresponding either to the desired cube cornerelement geometry in the finished sheeting or to a negative (inverted)copy thereof, depending upon whether the finished sheeting is to havecube corner pyramids or cube corner cavities (or both). The mold is thenreplicated using any suitable technique such as conventional nickelelectroplating to produce tooling for forming cube cornerretroreflective sheeting by processes such as embossing, extruding, orcast-and-curing. U.S. Pat. No. 5,156,863 (Pricone et al.) provides anillustrative overview of a process for forming tooling used in themanufacture of cube corner retroreflective sheeting. Known methods formanufacturing the master mold include pin-bundling techniques, laminatetechniques, and direct machining techniques. Each of these techniqueshas its own benefits and limitations.

In pin bundling techniques, a plurality of pins, each having a geometricshape such as a cube corner element on one end, are assembled togetherto form a master mold. U.S. Pat. No. 1,591,572 (Stimson) and U.S. Pat.No. 3,926,402 (Heenan) provide illustrative examples. Pin bundlingoffers the ability to manufacture a wide variety of cube corner geometryin a single mold, because each pin is individually machined. However,such techniques are impractical for making small cube corner elements(e.g. those having a cube height less than about 1 millimeter) becauseof the large number of pins and the diminishing size thereof required tobe precisely machined and then arranged in a bundle to form the mold.

In laminate techniques, a plurality of plate-like structures known aslaminae, each lamina having geometric shapes formed on one end, areassembled to form a master mold. Laminate techniques are generally lesslabor intensive than pin bundling techniques, because the number ofparts to be separately machined is considerably smaller, for a givensize mold and cube corner element. However, design flexibility suffersrelative to that achievable by pin bundling. Illustrative examples oflaminate techniques can be found in U.S. Pat. No. 4,095,773 (Lindner);International Publication No. WO 97/04939 (Mimura et al.); and U.S.application Ser. No. 08/886,074, “Cube Corner Sheeting Mold and Methodof Making the Same”, filed Jul. 2, 1997.

In direct machining techniques, series of grooved side surfaces areformed in the plane of a planar substrate to form a master mold. In onewell known embodiment, three sets of parallel grooves intersect eachother at 60 degree included angles to form an array of cube cornerelements, each having an equilateral base triangle (see U.S. Pat. No.3,712,706 (Stamm)). In another embodiment, two sets of grooves intersecteach other at an angle greater than 60 degrees and a third set ofgrooves intersects each of the other two sets at an angle less than 60degrees to form an array of canted cube corner element matched pairs(see U.S. Pat. No. 4,588,258 (Hoopman)). Direct machining techniquesoffer the ability to accurately machine very small cube corner elementsin a manner more difficult to achieve using pin bundling or laminatetechniques because of the latter techniques' reliance on constituentparts that can move or shift relative to each other, and that mayseparate from each other, whether during construction of the mold or atother times. Further, direct machining techniques produce large areastructured surfaces that generally have higher uniformity and fidelitythan those made by pin bundling or laminate techniques, since, in directmachining, a large number of individual faces are typically formed in acontinuous motion of the cutting tool, and such individual facesmaintain their alignment throughout the mold fabrication procedure.

However, a significant drawback to direct machining techniques has beenreduced design flexibility in the types of cube corner geometry that canbe produced. By way of example, the maximum theoretical total lightreturn of the cube corner elements depicted in the Stamm patentreferenced above is approximately 67%. Since the issuance of thatpatent, structures and techniques have been disclosed which greatlyexpand the variety of cube corner designs available to the designerusing direct machining. See, for example, U.S. Pat. No. 4,775,219(Appledorn et al.); U.S. Pat. No. 4,895,428 (Nelson et al.); U.S. Pat.No. 5,600,484 (Benson et al.); U.S. Pat. No. 5,696,627 (Benson et al.);and U.S. Pat. No. 5,734,501 (Smith). Some of the cube corner designsdisclosed in these later references can exhibit effective aperturevalues well above 67% at certain observation and entrance geometry.

Nevertheless, an entire class of cube corner elements, referred toherein as “preferred geometry” or “PG” cube corner elements, have upuntil now remained out of reach of known direct machining techniques. Asubstrate incorporating one type of PG cube corner element is shown inthe top plan view of FIG. 1. The cube corner elements shown there eachhave three square faces, and a hexagonal outline in plan view. One ofthe PG cube corner elements is highlighted in bold outline for ease ofidentification. The highlighted cube corner element can be seen to be aPG cube corner element because it has a non-dihedral edge (any one ofthe six edges that have been highlighted in bold) that is inclinedrelative to the plane of the structured surface, and such edge isparallel to adjacent nondihedral edges of neighboring cube cornerelements (each such edge highlighted in bold is not only parallel to butis contiguous with nondihedral edges of its six neighboring cube cornerelements).

Disclosed herein are methods for making geometric structures, such as PGcube corner elements, that make use of direct machining techniques. Alsodisclosed are molds to manufacture articles according to such methods,such articles characterized by having at least one specially configuredcompound face.

BRIEF SUMMARY

Structured surface articles such as molds or sheeting are formed on acompound substrate comprising a machined substrate and a replicatedsubstrate. In one embodiment, the structured surface is a cube cornerelement on a compound substrate. In another embodiment, the structuredsurface comprises a geometric structure that has a plurality of faces,where one face is located on the machined substrate and another face islocated on the replicated substrate. The geometric structure canoptionally be a cube corner element or a PG cube corner element.

In yet another embodiment, at least some of the faces comprise acompound face with a portion formed on the machined substrate and aportion formed on the substantially replicated substrate. A transitionline may separate the portion of a compound face located on the machinedsubstrate from the portion located on the replicated substrate. Theportion of the compound face on the machined substrate and the portionon the replicated substrate typically have angular orientations thatdiffers by less than 10 degrees of arc.

Another embodiment is directed to a geometric structure having aplurality of faces disposed on a compound substrate. The compoundsubstrate comprises a machined substrate having a structured surface anda substantially replicated substrate bonded along only a portion of aninterface with the machined substrate.

In another embodiment, the compound substrate comprises a substantiallyreplicated substrate having a structured surface and a discontinuousmachined substrate covering only a portion of the structured surface.The compound substrate also comprises at least one geometric structurehaving at least one face disposed on the structured surface and at leastanother face disposed on the machined substrate.

Another embodiment is directed to a compound substrate comprising asubstantially replicated substrate and a machined substrate. Thereplicated substrate has a structured surface and the machined substratedisposed in discrete pieces on the structured surface.

Another embodiment is directed to a compound mold having a structuredsurface comprising cavities formed in a replicated substrate and aplurality of pyramids bordering the cavities that are machined at leastin part in a machined substrate of the compound substrate.

Cube corner elements, and structured surfaces incorporating an array ofsuch elements, are disclosed wherein at least one face of the cubecorner element terminates at a nondihedral edge of such element, theface comprising two constituent faces disposed on opposed sides of atransition line that is nonparallel to the nondihedral edge. The cubecorner element can comprise a PG cube corner element where some or allof such elements comprise two constituent faces disposed on opposedsides of a transition line that is nonparallel to the respectivenondihedral edge and the transition line comprises an interface betweentwo adjacent layers of a compound substrate. In an array of neighboringcube corner elements, each cube corner element in the array can have atleast one face configured as described above. Further, the cube cornerelements can be made very small (well under 1 mm cube height) due to thedirect machining techniques employed.

Also disclosed is a method of making a structured surface articlecomprising a geometric structure having a plurality of faces. The methodcomprises the steps of forming an array of geometric structures in afirst surface of a machined substrate; passivating selected locations ofthe first surface of the machined substrate; forming a replicatedsubstrate of the machined substrate to form a compound substrate;forming an array of second geometric structures on a second surfaceopposite the first surface on the machined substrate; and removingselected portions from the second surface of the machined substrate toform an array of neighboring cube corner elements. The cube cornerelements can be PG cube corner elements.

In another embodiment, the method of making a structured surface articlecomprises the steps of forming an array of geometric structures in afirst surface of a machined substrate; passivating selected locations ofthe first surface of the machined substrate; forming a replicatedsubstrate of the machined substrate to form a compound substrate;forming an array of second geometric structures on a second surfaceopposite the first surface on the machined substrate; and removingselected portions from the second surface of the machined substrate toform a geometric structure having a plurality of faces, wherein at leastone of the faces is located on the machined substrate and at least oneof the faces is located on the replicated substrate.

In another embodiment, the method of making a geometric structure in anarticle comprises providing a compound substrate having a structuredsurface formed along an internal interface between two substrates; andforming grooved side surfaces in an exposed surface of the compoundsubstrate to form a geometric structure, the geometric structurecomprising a portion of the internal interface and a portion of thegrooved side surfaces.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a plan view of a structured surface comprising one type of PGcube corner element array, known from the PRIOR ART.

FIG. 2 is a perspective view of an assembly including a machinedsubstrate.

FIG. 3 is a sectional view of the substrate of FIG. 2.

FIG. 4 is a perspective view of the substrate of FIG. 2 after a firstmachining operation.

FIG. 5 is a close-up perspective view of a portion of the machinedsubstrate illustrated in FIG. 4.

FIG. 6 is a sectional view of an assembly including a compoundsubstrate.

FIG. 6 a is an enlarged section of the compound substrate of FIG. 6.

FIG. 7 is a perspective view of the assembly of FIG. 6 with one of themachining bases removed.

FIG. 8 is a perspective view of the assembly of FIG. 7 with a portion ofa blank surrounding the machined substrate removed.

FIG. 9 is cross-sectional view of the machining of the compoundsubstrate of FIG. 7.

FIG. 10 is a perspective view of the compound substrate of FIG. 8 afterthe second machining operation.

FIG. 11 is a top view of FIG. 10. FIGS. 12-14 are top plan views ofstructured surfaces having canted PG cube corner elements, such surfacesbeing capable of fabrication using the methods discussed in connectionwith FIGS. 2-11.

FIG. 15 is a top plan view of an alternate machined substrate inaccordance with the present invention.

FIG. 16 is a sectional view of the substrate of FIG. 15.

FIG. 17 is a sectional view of the substrate of FIG. 15 with apassivated surface.

FIG. 18 is a top plan view of the substrate of FIG. 17 with portions ofthe passivated surface removed.

FIG. 19 is a sectional view of the substrate of FIG. 18.

FIG. 20 is a sectional view of an assembly including a compoundsubstrate.

FIG. 21 is a top plan view of the machining of the compound substrate ofFIG. 20.

FIG. 22 is a sectional view of the substrate of FIG. 21.

FIG. 23 is a top plan view of the compound substrate of FIG. 21 afterthe second machining operation.

In the drawings, the same reference symbol is used for convenience toindicate elements that are the same or that perform the same or asimilar function.

DETAILED DESCRIPTION OF THE ILLUSTRATIVE EMBODIMENTS

FIGS. 2 and 3 illustrate an assembly 20 useful for making a structuredsurface (see FIGS. 9-10) in accordance with the present invention. Theassembly 20 includes a blank 22 bonded to a first machining base 24 by afirst bonding layer 26. In the illustrated embodiment, the blank 22 is acontinuous structure that includes a deck 27 and a series of referencepads 30 a, 30 b, 30 c, 30 d, 30 e, 30 f (collectively referred to as 30)that extend above surface 32. In one embodiment, the deck 27 has aheight 34 generally equal to a height 36 of the reference pads 30. Thenumber of reference pads 30 can vary depending upon the application. Inan alternate embodiment, the deck 27 and the reference pads 30 can bediscrete elements bonded to the first machining base 24, rather than thecontinuous blank 22 shown in FIG. 2.

Blank 22 is composed of a material that can be scribed, cut, orotherwise machined without significant post-machining deformation andwithout substantial burring. This is to ensure that the machined faces,or replications thereof in other substrates, can function as effectiveoptical reflectors. The blank 22 may be constructed from variousmaterials, such as copper, nickel, aluminum, acrylic, or other polymericmaterials. Further discussion on suitable substrate materials is givenbelow. In one embodiment, the blank 22 is a thin metal sheet materialapproximately 0.030 inches thick.

The blank 22 is bonded to a first machining base 24 using a suitablebonding layer 26, such as epoxy, wax, thermoform or thermoset adhesives,and the like. In the illustrated embodiment, the first machining base 24is a metal plate approximately 2.54 centimeters (1.0 inch) thick. Thefirst machining base 24 supports the relatively thin blank 22 andprovides reference surfaces 38 for subsequent machining operations.Although the circular shape of the assembly 20 is convenient forsubsequent electroplating operations, the circular shape is notrequired.

FIG. 4 depicts the machining operation to form a machined substrate 28in the deck portion 27 of the blank 22. Cutting tools 40 a, 40 b, 40 c(collectively referred to as 40) move along the deck 27 (see FIG. 2) toform a structured surface 50 of machined substrate 28, whether by motionof the cutting tools or the substrate or both, to form groove sidesurfaces (see FIG. 5). The cutting tool 40 a forms reference grooves 44c, 44 f in respective reference pads 30 c, 30 f, cutting tool 40 b formsreference grooves 44 a, 44 d in respective reference pads 30 a, 30 d,and cutting tool 40 c forms reference grooves 44 b, 44 e in respectivereference pads 30 b, 30 e. A circular reference groove 46 a, 46 b, 46 c,46 d, 46 e, 46 f concentric with the center of the machined substrate 28is optionally formed in each of the respective reference pads 30.Reference marks 43 may optionally be formed on the edge of the modifiedblank 22′ to assist in locating the compound substrate 82 to perform thecutting operations illustrated in FIG. 7.

Each tool 40 is depicted as a so-called “half-angle” tool, whichproduces grooved side surfaces as it progresses through the materialrather than a pair of opposed groove side surfaces, although this is notnecessary. In the illustrated embodiment, one of the grooved sidesurfaces is substantially vertical (see FIG. 5). Consistent with directmachining procedures, cutting tools 40 move along axes 42 a, 42 b, 42 cthat are substantially parallel to the x-y reference plane defined bythe reference surface 38, thus ensuring that the respective groove sidesurfaces also extend along axes that are substantially parallel to thereference plane. In the illustrated embodiment, each of the axes 42 a,42 b, 42 c intersect two of the reference pads 30. Preferably, the axes42 a, 42 b, 42 c are carefully positioned and the tool orientationcarefully selected so that the groove side surfaces have a generallyuniform depth.

It should be noted that although three cutting tools are shown in FIG.4, a single cutting tool could be used. The cutting tool can be made ofdiamond or other suitably hard material. The machined faces can beformed by any one of a number of known material removal techniques, forexample: milling, where a rotating cutter, spinning about its own axis,is tilted and drawn along the surface of the substrate; fly-cutting,where a cutter such as a diamond is mounted on the periphery of arapidly rotating wheel or similar structure which is then drawn alongthe surface of the substrate; ruling, where a nonrotating cutter such asa diamond is drawn along the surface of the substrate; and grinding,where a rotating wheel with a cutting tip or edge is drawn along thesurface of the substrate. Of these, preferred methods are those offly-cutting and ruling. It is not critical during the machiningoperation whether the cutting tool, the substrate, or both aretranslated relative to the surroundings. Full-angle cutting tools arepreferred when possible over half-angle tools because the former areless prone to breakage and allow higher machining rates. Finally,cutting tools having a curved portion or portions can be used in thedisclosed embodiments to provide non-flat (curved) surfaces or faces inorder to achieve desired optical or mechanical effects.

FIG. 5 shows an enlarged section of the structured surface 50 machinedin the machined substrate 28 illustrated in FIG. 4. Structured surface50 includes faces 54 arranged in groups of three that form cube cornerpyramids 56. Interspersed between cube corner pyramids 56 on structuredsurface 50 are protrusions 58. The protrusions 58 as shown each havethree mutually perpendicular side surfaces 60, three generally verticalsurfaces 61, and a top surface 62. Depending on the procedure used tomake the structured surface 50, the generally vertical surfaces 61 ofthe protrusions 58 can be inclined to a greater or lesser extent awayfrom the vertical. In the illustrated embodiment, the cube cornerpyramids 56 cover about 50% of the machined substrate and theprotrusions 58 cover the other 50% of the substrate.

The structured surface 50 is then cleaned and passivated. Thepassivation step comprises applying a release layer or modifying thesurface 50 to permit separation of a subsequent replicated substrate 70(see FIG. 6). In an embodiment where the blank 22 is constructed frommetal, such as copper, the structured surface 50 can be passivated withpotassium dichromate or other passive solutions. In an embodiment wherethe blank 22 is constructed from acrylic or another polymeric material,vapor coated or chemically deposited silver can be used to create therelease layer. The passivation step can be modified depending upon thematerial used for the machined substrate 28 and the replicated substrate70.

In order to permit selective adhesion of the replicated substrate 70 tothe structured surface 50, the top surfaces 62 of the protrusions 58 aretreated. In one embodiment, the top surfaces 62 are abraded. Abrasion ofthe top surfaces 62 can be accomplished using a planarization process,fly cutting, or a variety of other processes.

FIGS. 6 and 6 a illustrate an assembly 81 that results after forming areplicated substrate 70 over the machined substrate 28 and the referencepads 30. Electroplating, casting a filler material, and a variety ofother techniques can form the replicated substrate 70. The thickness ofthe replicated substrate 70 is a matter of design choice. In theillustrated embodiment, the replicated substrate 70 has a thickness ofabout 2 times the height of the desired cube corner elements.

As best illustrated in FIG. 6 a, due to the previous passivation andabrasion steps, the replicated substrate 70 adheres to the structuredsurface 50 along the top surface 62 of the protrusions 58, but not alongthe passivated surfaces of the pyramids 56 and the side surfaces 60, 61of the protrusions 58. Portions of the replicated substrate 70 protrudeinto the machined substrate 28 to form a compound substrate 82 (see alsoFIG. 9). A second machining base 74 is bonded to rear surface 76 of thereplicated substrate 70 using a suitable bonding layer 78. Like thefirst machining base 24, the second machining base 74 includes referencesurfaces 80 to aid in subsequent machining steps. The first machiningbase 24 and bonding layer 26 are no longer needed for the process andare removed from the assembly 20.

FIG. 7 is a perspective view of an assembly 81 comprising the modifiedblank 22′ (machined substrate 28 and reference pads 30) selectivelybonded to the replicated substrate 70. The replicated substrate 70 isbonded to the second machining base 74 by the bonding layer 78. In theillustrated embodiment, rear surface 71 of the modified blank 22′ issubstantially flat. The compound substrate 82 and reference pads 30embedded in the assembly 81 are shown in phantom for purposes ofillustration only.

A series of four cuts are made around the perimeter P1, P2, P3, P4 ofcompound substrate 82, permitting the portions of the modified blank 22′surrounding the machined substrate 28 to be removed from the assembly81. Reference marks 43 may optionally be used to locate the compoundsubstrate 82. The passivation layer facilitates removal of this wastematerial. In an embodiment where the blank 22 and replicated substrate70 are constructed from metal, the portion of the blank 22 surroundingthe machined substrate 28 is a thin layer that can be peeled from thereplicated substrate 70.

FIG. 8 is a perspective view of a modified assembly 83 with the portionsof the blank 22 surrounding the compound substrate 82 removed. Surface85 is of the replicated substrate 70. Surface 90, which extends abovethe surface 85, is the back surface of the machined substrate 28.Reference pad replicas 84 a, 84 b, 84 c, 84 d, 84 e, 84 f (collectivelyreferred to as 84) of the reference pads 30 define cavities in thesurface 85. The reference pad replicas 84 a, 84 d have respectiveparallel ridges 86 a, 86 d, replicas 84 b, 84 e have respective parallelridges 86 b, 86 e, and replicas 84 c, 84 f have respective parallelridges 86 c, 86 f (collectively referred to as 86). Each of thereference pad replicas 84 has a ridge 88 a, 88 b, 88 c, 88 c, 88 d, 88e, 88 f (collectively referred to as 88), respectively, defining acircle concentric with the center of the compound substrate 82. In theillustrated embodiment, the tops of the ridges 86, 88 are generallycoplanar with the surface 85.

FIG. 9 is a schematic illustration of the machining step performed onthe back surface 90 of the machined substrate 28. In the illustratedembodiment, the compound substrate 82 comprises the machined substrate28 and the un-separated replicated substrate 70. The interface 92between the structured surface 50 and the replicated substrate 70 isindicated by dashed line. Bonding at the interface 92, however, islimited to the abraded top surfaces 62 of the protrusions 58. Thepassivation layer prevents or minimizes adhesion along the remainder ofthe interface 92, such as along the pyramids 56 or the side surfaces 60,61 of the protrusions 58.

The machining step illustrated in FIG. 4 is then performed on the backsurface 90 of the machined substrate 28 using the ridges 86, 88 asreference points to guide tool 101. The tool 101 may or may not be ahalf-angle tool. In an embodiment where the machined substrate 28 and/orthe replicated substrate 70 are formed from a transparent orsemi-transparent material, or where the interface between the machinedsubstrate 28 and replicated substrate 70 can be viewed along theperimeter P1, P2, P3, P4 of compound substrate 82, the reference padreplicas 84 may be unnecessary. That is, alignment of the tools 42 a, 42b, 42 c can be accomplished without resort to the reference pad replicas84. Where the machined substrate 28 is formed from an opaque materialsuch as metal, the reference pad replicas 84 (and particularly theridges 86) provide precise reference points so that the machining stepillustrated in FIG. 9 can be performed.

After cuts are made along all three axes 42 a, 42 b, 42 c, wasteportions 94 of the machined substrate 28 fall away or are removed,leaving a cube corner cavity 118 in the replicated substrate 70. In someembodiments, the tool 101 may cut into the replicated substrate 70 suchthat the replicated substrate may include a replicated or formed portionand a machined portion. The distal ends or top surfaces 62 of thediscrete pieces or protrusions 58 from the machined substrate 28 arebonded to the replicated substrate 70. Bottom or proximal portions ofthe protrusions 58 are machined to form cube corner pyramids 120 a. Theprotrusions 58 on the machined substrate 28 remain embedded in thereplicated substrate 70. Once all of the waste portions 94 of themachined substrate 28 are removed from the replicated substrate 70, thecube corner pyramids 120 a and cube corner cavities 118 form a geometricstructured surface 100 with an array of PG cube corner elements (seeFIG. 10).

FIG. 10 is a view of a geometric structured surface 100 on compoundsubstrate 82 after all groove side surfaces have been formed. Each ofthe cube corner cavities 118 has three replicated faces 116 a, 116 b,116 c and each of the cube corner pyramids 120 a has three machinedfaces 126 a, 126 b, 126 c, configured approximately mutuallyperpendicular to each other. In the case where the three faces of a cubecorner pyramid 120 a are substantially aligned with adjacent faces 116of cavities 118, and where such cavities 118 have a common orientation,the three faces of cube corner pyramid 120 a (when consideredseparately) form a “truncated” cube corner pyramid. Such a pyramid ischaracterized by having exactly three nondihedral edges that form a“base triangle” in the plane of the structured surface.

Each of the three faces 126 a-c of the cube corner pyramids 120 a aremachined to be substantially aligned with the nearest face 116 of anadjacent cube corner cavity 118. Consequently, each new cube cornercavity 132 comprising one replicated cube corner cavity 118 and onemachined face 126 from each of its neighboring geometric structures 120a. Reference numeral 132 a shows in bold outline one such cube cornercavity 132. A given face of one of the cube corner cavities 132comprises one face of a cube corner cavity 118 formed in the replicatedsubstrate 70 and one of the faces 126 a, 126 b, or 126 c machined in themachined substrate 28. As will be discussed infra, faces 116 of the cubecorner cavity 118 are machined in the replicated substrate 70.Therefore, each cube corner cavity 132 comprises a compound face made upof a portion substantially formed or replicated in the replicatedsubstrate 70 and a portion machined in the machined substrate 28separated by a transition line 130. The transition lines 130 lie alongthe boundary or interface between the machined substrate 28 and thereplicated substrate 70.

One can also identify new cube corner pyramids 134 formed on thestructured surface shown in FIG. 10. Each cube corner pyramid 134comprises one geometric structure 120 a, which is a cube corner pyramid,and one face each of its neighboring cube corner cavities 118. Each faceof one of the pyramids 134 is a compound face comprising a face 116 ofone of the cavities 118 in the replicated substrate 70 and a machinedface from structure 120 a formed from the machined substrate 28.Reference numeral 134 a shows in bold outline of one such cube cornerpyramid 134. Note that the reference points 122 locate the uppermostextremities or peaks of the pyramids 134. Both cube corner pyramids 134and cube corner cavities 132 are PG cube corner elements, since bothhave a face terminating at a nondihedral edge of the cube cornerelement, such nondihedral edge being nonparallel to reference plane x-y.

FIG. 11 shows a top view of the structured surface of FIG. 10.Transition lines 130 are drawn narrower than other lines to aid inidentifying the PG cube corner elements, i.e. cube corner cavities 132and cube corner pyramids 134. The compound faces of such PG cube cornerelements extend across opposite sides of the transition lines 130separating discrete pieces of the machined substrate 28 from thereplicated substrate 70, to which they are bonded. In the illustratedembodiment, all transition lines 130 lie in a common plane referred toas a transition plane, which in the case of this embodiment is coplanarwith the x-y plane. The faces of the structured surface machined in themachined substrate 28 are disposed on one side of the transition planeand the faces machined in the replicated substrate 70 are disposed onthe other side.

The machined cube corner article of FIGS. 10-11 can itself function as aretroreflective article, both with respect to light incident from above(by virtue of cube corner cavities 132) and, where the substrate is atleast partially transparent, with respect to light incident from below(by virtue of cube corner pyramids 134). In either case, depending uponthe composition of the substrate, a specularly reflective thin coatingsuch as aluminum, silver, or gold can be applied to the structuredsurface to enhance the reflectivity of the compound faces. In the casewhere light is incident from below, reflective coatings can be avoidedin favor of an air interface that provides total internal reflection.

More commonly, however, the compound substrate of FIGS. 10-11 is used asa mold from which end-use retroreflective articles are made, whetherdirectly or through multiple generations of molds, using conventionalreplication techniques. Each mold or other article made from thecompound substrate will typically contain cube corner elements having atleast one face terminating at a nondihedral edge of the cube cornerelement, the at least one face comprising two constituent faces disposedon opposed sides of a transition line, the transition line beingnonparallel to such nondihedral edge. As seen from FIGS. 10-11,transition lines 130 lie in the transition plane coincident with the x-yplane, whereas nondihedral edges shown in bold for both PG cube cornercavity 132 and PG cube corner pyramid 134 are inclined relative to thex-y plane. It is also possible to fabricate surfaces where thetransition lines do not all lie in the same plane, by forming grooveside surfaces at different depths in the substrate.

Transition lines can in general take on a great variety of forms,depending upon details of the cutting tool used and on the degree towhich the motion of the cutting tool is precisely aligned with otherfaces in the process of forming groove side surfaces. Although in manyapplications transition lines are an artifact to be minimized, in otherapplications they can be used to advantage to achieve a desired opticalresult such as a partially transparent article. A detailed discussion ofvarious transition line configurations is set forth in commonly assignedU.S. patent application Ser. No. 09/515,120 filed on the same dateherewith, entitled Structured Surface Articles Containing GeometricStructures with Compound Faces and Methods for Making Same, which isincorporated by reference.

A wide variety of structured surfaces can be fabricated using thepresent compound substrate 82 and the machining technique describedabove. The PG cube corner elements of FIG. 11 each have a symmetry axisthat is perpendicular to the x-y reference plane of the structuredsurface. Cube corner elements typically exhibit the highest opticalefficiency in response to light incident on the element roughly alongthe symmetry axis. The amount of light retroreflected by a cube cornerelement generally drops as the incidence angle deviates from thesymmetry axis. FIG. 12 shows a top plan view of a structured surface 136similar to that of FIG. 11, extending along the x-y plane, except thatthe PG cube corner elements of FIG. 12 are all canted such that theirsymmetry axes are tilted with respect to the normal of the structuredsurface. The symmetry axis for each PG cube corner cavity 146 in FIG. 12lies in a plane parallel to the y-z plane, having a vertical componentin the +z direction (out of the page) and a transverse component in the+y direction. Symmetry axes for the PG cube corner pyramids 148 of FIG.12 point in the opposite direction, with components in the −z and −ydirections. In fabricating surface 136, a compound substrate is usedwherein the protrusions of generally triangular cross-section areisosceles in shape, rather than equilateral as in FIG. 1.

Four distinct types of cube corner elements are present on thestructured surface 136: truncated cube corner cavities formed inreplicated substrate 70 and a triangular outline in plan view; truncatedcube corner pyramids having faces machined in discrete pieces of themachined substrate 28 and triangular outline; PG cube corner cavitieshaving compound faces and a hexagonal outline; and PG cube cornerpyramids, also having compound faces and a hexagonal outline. Arepresentative cube corner cavity formed in the replicated substrate 70is identified in FIG. 12 by bold outline 140, and a representative cubecorner pyramid machined in the machined substrate 28 is identified bybold outline 142. Transition lines 144 separate machined from formed orreplicated faces, and all such lines 144 lie in a transition planeparallel to the x-y plane. In other embodiments, the transition linesmay lie parallel to a transition plane but not be coplanar. Selectedfaces of cavities 140 and pyramids 142 form canted PG cube cornerelements, in particular canted PG cube corner cavities 146 and canted PGcube corner pyramids 148. Reference points 122, as before, identifylocalized tips or peaks disposed above the x-y plane.

FIG. 13 shows a structured surface 136 a similar to that of FIG. 12, andlike features bear the same reference numeral as in FIG. 12 with theadded suffix “a”. PG cube corner elements of FIG. 13 are canted withrespect to the normal of structured surface 136 a, but in a differentdirection compared to that of the PG cube corner elements of FIG. 12.The symmetry axis for each PG cube corner cavity 146 a is disposed in aplane parallel to the y-z plane, and has a vertical component in the +zdirection and a transverse component in the −y direction.

FIG. 14 shows a structured surface similar to that of FIGS. 12 and 13,and like features bear the same reference numeral as in FIG. 12 with theadded suffix “b”. PG cube corner elements in FIG. 14 are also canted,but, unlike the PG cube corner elements of FIGS. 12 and 13, the degreeof cant is such that the outline in plan view of each PG cube cornerelement has no mirror-image plane of symmetry. The cube corner cavitiesof FIG. 14 each have a symmetry axis that has components in the +z, +y,and −x direction. It will be noted that the triangles formed bytransition lines 144 (FIG. 12) are isosceles triangles each having onlyone included angle less than 60 degrees; triangles formed by lines 144 a(FIG. 13) are isosceles triangles each having only one included anglegreater than 60 degrees; and triangles formed by lines 144 b (FIG. 14)are scalene triangles. Representative values in degrees for the includedangles of triangles defined by transition lines 144 a are, respectively:(70, 70, 40); (80, 50, 50); and (70, 60, 50).

The embodiments discussed above have associated therewith anasymmetrical entrance angularity (i.e., when rotated about an axiswithin the plane of the sheeting). Embodiments with symmetrical entranceangularity are also possible, such as the matched-pair cube cornerstructure discussed in connection with FIGS. 15-23.

FIGS. 15 and 16 depict an alternate machined substrate 200 in accordancewith the present invention. The machined substrate 200 is bonded to afirst machining base 202 by a first bonding layer 204. Two sets ofgrooves 206, 208 parallel to axis 207 a 207 b, respectively, are formedusing tools 201 a, 201 b to define a machined surface 212. In theillustrated embodiment, the machined surface 212 includes faces 213arranged in groups of four that form four-sided pyramids 210 having anapex or reference point 215. The four-sided pyramids 210 are arranged inrows 217, 222, 223. Other geometric structures 211 are also formed bythe grooves 206, 208.

As illustrated in sectional view FIG. 17, the machined surface 212 isthen cleaned and passivated. The passivation step comprises applying arelease layer or making a surface modification 216 (referred tocollectively as “passivated surface”) on the machined surface 212 topermit separation of a subsequent replicated substrate 214 (see FIG.20). In one embodiment, the passivated surface is formed on only aportion of the machined surface 212.

As illustrated in FIGS. 18 and 19, additional grooves 220 a, 220 b, 220c (referred to collectively as 220) are formed in the machined surface212 parallel to axis 207 c using tool 201 c in order to remove portionsof some of the geometric structures 211. The grooves 220 also removesome of the surface modification 216 to permit selective adhesion of thereplicated substrate 214 (see FIG. 20) to the machined surface 212. Asbest illustrated in FIG. 19, the passivated surface 216 is not presentalong flat regions 228 or along side walls 230, while the passivatedsurface 216 on faces 213 is substantially intact.

FIG. 20 illustrates an assembly 232 that results after forming areplicated substrate 214 over the machined substrate 200′.Electro-plating, casting a filler material, and a variety of othertechniques can form the replicated substrate 214. Due to the previouspassivation step, the replicated substrate 214 adheres to the flatregions 228 and side walls 230, but not along the passivated surfaces216. Portions 234 of the replicated substrate 214 protrude into, andbond with, the machined substrate 200′ along surfaces 228, 230 to form acompound substrate 236. A second machining base 250 is bonded to rearsurface 252 of the replicated substrate 214 using a suitable bondinglayer 254. Like the first machining base 202, the second machining base250 includes reference surfaces (see FIG. 3) to aid in subsequentmachining steps. The first machining base 202 and bonding layer 204 areno longer needed for the process and are removed from the assembly 232.The second machining base 250 supports the compound substrate 236 duringmachining of the back surface 260, discussed below.

FIGS. 21 and 22 illustrate the machining step performed on the backsurface 260 of the compound substrate 236. Grooves 268 a, 268 b, 268 care formed along axes 270 a, 270 b, 270 c using tools 272 a, 272 b, 272c. The grooves 268 a, 268 b, 268 c may extend into the replicatedsubstrate 214. Waste portions 274 are not bonded to the replicatedsubstrate 214 because of the passivation layer 216. Consequently, afterthe grooves 268 are made along all three axes 270, waste portions 274fall away or are removed, leaving four-sided cavities 276 in thereplicated substrate 214.

Discrete pieces or portions 278, 280 of the compound substrate 236,however, are bonded to the replicated substrate 214 along surfaces 230.Bottom or proximal portions of the portions 278, 280 are machined toform three-sided pyramids 282. The portions 278, 280 of the machinedsubstrate 200′ remain embedded in the replicated substrate 214 portionof the compound substrate 236. Once all of the waste portions 274 of thecompound substrate 236 are removed from the replicated substrate 214,thus exposing all of the four-sided cavities 276, the three-sidedpyramids 282 and four-sided cavities 276 form a geometric structuredsurface 290 comprising an array of PG cube corner elements (see FIG.23).

In an embodiment where the machined substrate 200′ and/or the replicatedsubstrate 214 are formed from a transparent or semi-transparentmaterial, or where the interface between the machined substrate 200′ andreplicated substrate 214 can be viewed along the perimeter of compoundsubstrate 236, reference pads such as illustrated in connection withFIGS. 2-8 may be unnecessary. That is, alignment of the tools can beaccomplished without resort to the reference pad. Where the machinedsubstrate 200′ is formed from an opaque material such as metal,reference pads such as illustrated in FIG. 2 provide precise referencepoints so that the machining step illustrated in FIG. 21 can beperformed.

FIG. 23 illustrates the geometric structured surface 290 after allgroove side surfaces have been formed. This geometry results in twodifferent types of PG cube corner elements on the structured surface.Cube corner pyramid 296 has face g and compound faces h, h′; i, i′separated by transition lines a and b, respectively. Cube corner pyramid298 has face j and compound faces k, k′; 1,1′ separated by transitionlines c and d, respectively. Faces g and j are polygons with more thanthree sides. Consequently, in the top view of FIG. 23, the cube cornerpyramids 296, 298 each have a rectangular shape as shown by therespective dashed outlines, rather than a hexagonal outline as depictedin FIGS. 10-14. In an embodiment where the grooves 272 c are all of thesame depth, the cube corner elements 296 and 298 are opposing or matchedpair cube corner elements that provide symmetric entrance angularity.Depending upon the aspect ratio, the plan view rectangular outlines ofthe cube corner elements can also include a square outline.

Cube corner elements of FIG. 23 can be (forward or backward) canted oruncanted as desired. Producing cube corner elements that are canted to agreater or lesser degree is accomplished by tailoring the shape of thediamond-shaped protrusions and then the orientation of the groove sidesurfaces (g, h, i, j, k, l) to be in conformance with the desired degreeof canting. If canting is used, then such matched pairs can, in keepingwith principles discussed in U.S. Pat. No. 4,588,258 (Hoopman), U.S.Pat. No. 5,812,315 (Smith et al.), and U.S. Pat. No. 5,822,121 (Smith etal.), give rise to widened retroreflective angularity so that an articlehaving the structured surface will be visible over a widened range ofentrance angles.

During the present machining process, the cutting tool removes arelatively large amount of material because the angle between thesteeply inclined side wall and the subsequent machined face is often inexcess of 10 degrees, typically ranging from about 10 to about 45degrees. Some of the groove side surfaces can then be formed in such amodified machined substrate by leaving more material on the cavities orprotrusions during either or both machining steps, thereby reducing toolforces which could detrimentally cause distortions. Another benefit isless wear on the cutting tool. A modified machined substrate can also beused as a master from which future generations of positive/negativemolds can be made. Various geometric configurations for modifiedmachined substrate are disclosed in commonly assigned U.S. patentapplication Ser. No. 09/515,120 (U.S. Pat. No. 6,540,367)filed on thesame date herewith, entitled Structured Surface Articles ContainingGeometric Structures with Compound Faces and Methods for Making Same,which is incorporated by reference.

The cube corner elements disclosed herein can be individually tailoredso as to distribute light retroreflected by the articles into a desiredpattern or divergence profile, as taught by U.S. Pat. No. 4,775,219(Appledorn et al.). For example, compound faces that make up the PG cubecorner elements can be arranged in a repeating pattern of orientationsthat differ by small amounts, such as a few arc-minutes, from theorientation that would produce mutual orthogonality with the other facesof cube corner element. This can be accomplished by machining grooveside surfaces (both those that ultimately become the faces in thefinished mold below the transition plane as well as those that becomefaces in the finished mold above the transition plane) at angles thatdiffer from those that would produce mutually orthogonal faces by anamount known as a “groove half-angle error”. Typically the groovehalf-angle error introduced will be less than ±20 arc minutes and oftenless than ±5 arc minutes. A series of consecutive parallel groove sidesurfaces can have a repeating pattern of groove half-angle errors suchas abbaabba . . . or abcdabcd . . . , where a, b, c, and d are uniquepositive or negative values. In one embodiment, the pattern of groovehalf-angle errors used to form faces in the finished mold above thetransition plane can be matched up with the groove half-angle errorsused to form faces in the finished mold below the transition plane. Inthis case, the portions of each compound face on the machined substrateand the replicated substrate will be substantially angularly alignedwith each other. In another embodiment, the pattern used to form one setof faces can differ from the pattern used to form the other, as wherethe faces below the transition plane incorporate a given pattern ofnonzero angle errors and faces above the transition plane incorporatesubstantially no angle errors or a different pattern of non-zero errors.In this latter case, the portions of each compound face on the machinedsubstrate and the replicated substrate will not be precisely angularlyaligned with each other.

Advantageously, such substrates can serve as a master substrate fromwhich future generations of positive/negative molds can be made, allhaving the same general shape of cube corner element in plan view buthaving slightly different face configurations. One such daughter moldcan incorporate cube corner elements that each have compound faces whoseconstituent faces are aligned, the compound faces all being mutuallyperpendicular to the remaining faces of the cube corner element. Anothersuch daughter mold can incorporate cube corner elements that also havecompound faces whose constituent faces are aligned, but the compoundfaces can differ from orthogonality with remaining faces of the cubecorner element. Still another such daughter mold can incorporate cubecorner elements that have compound faces whose constituent faces are notaligned. All such daughter molds can be made from a single master moldwith a minimal amount of material removed by machining.

The working surface of the mold substrates can have any suitablephysical dimensions, with selection criteria including the desired sizeof the final mold surface and the angular and translational precision ofthe machinery used to cut the groove surfaces. The working surface has aminimum transverse dimension that is greater than two cube cornerelements, with each cube corner element having a transverse dimensionand/or cube height preferably in the range of about 25 μm to about 1 mm,and more preferably in the range of about 25 μm to about 0.25 mm. Theworking surface is typically a square several inches on a side, withfour inch (10 cm) sides being standard. Smaller dimensions can be usedto more easily cut grooves in registration with formed surfaces over thewhole structured surface. The substrate thickness can range from about0.5 to about 2.5 mm. (The measurements herein are provided forillustrative purposes only and are not intended to be limiting.) A thinsubstrate can be mounted on a thicker base to provide rigidity. Multiplefinished molds can be combined with each other e.g. by welding in knowntiling arrangements to yield a large tiled mold that can then be used toproduce tiled retroreflective products.

In the manufacture of retroreflective articles such as retroreflectivesheeting, the structured surface of the machined substrate is used as amaster mold that can be replicated using electroforming techniques orother conventional replicating technology. The structured surface caninclude substantially identical cube corner elements or can include cubecorner elements of varying sizes, geometry, or orientations. Thestructured surface of the replica, sometimes referred to in the art as a‘stamper’, contains a negative image of the cube corner elements. Thisreplica can be used as a mold for forming a retroreflective article.More commonly, however, a large number of suitable replicas areassembled side-by-side to form a tiled mold large enough to be useful informing tiled retroreflective sheeting. Retroreflective sheeting canthen be manufactured as an integral material, e.g. by embossing apreformed sheet with an array of cube corner elements as described aboveor by casting a fluid material into a mold. See, JP 8-309851 and U.S.Pat. No. 4,601,861 (Pricone). Alternatively, the retroreflectivesheeting can be manufactured as a layered product by casting the cubecorner elements against a preformed film as taught in PCT applicationNo. WO 95/11464 (Benson, Jr. et al.) and U.S. Pat. No. 3,684,348(Rowland) or by laminating a preformed film to preformed cube cornerelements. By way of example, such sheeting can be made using a nickelmold formed by electrolytic deposition of nickel onto a master mold. Theelectroformed mold can be used as a stamper to emboss the pattern of themold onto a polycarbonate film approximately 500 μm thick having anindex of refraction of about 1.59. The mold can be used in a press withthe pressing performed at a temperature of approximately 175° to about200° C.

The various mold substrates discussed above can generally be categorizedinto two groups: replicated substrates, which receive at least part oftheir structured surface by replication from a prior substrate, and bulksubstrates, which do not. Suitable materials for use with bulk moldsubstrates are well known to those of ordinary skill in the art, andgenerally include any material that can be machined cleanly without burrformation and that maintains dimensional accuracy after grooveformation. A variety of materials such as machinable plastics or metalsmay be utilized. Acrylic is an example of a plastic material; aluminum,brass, electroless nickel, and copper are examples of useable metals.

Suitable materials for use with replicated mold substrates that are notsubsequently machined are well known to those of ordinary skill in theart, and include a variety of materials such as plastics or metals thatmaintain faithful fidelity to the prior structured surface. Thermallyembossed or cast plastics such as acrylic or polycarbonate can be used.Metals such as electrolytic nickel or nickel alloys are also suitable.

Suitable materials for use with replicated mold substrates whosestructured surface is subsequently machined are also well known to thoseof ordinary skill in the art. Such materials should have physicalproperties such as low shrinkage or expansion, low stress, and so onthat both ensure faithful fidelity to the prior structured surface andthat lend such materials to diamond machining. A plastic such as acrylic(PMMA) or polycarbonate can be replicated by thermal embossing and thensubsequently diamond machined. Suitable hard or soft metals includeelectrodeposited copper, electroless nickel, aluminum, or compositesthereof.

With respect to retroreflective sheeting made directly or indirectlyfrom such molds, useful sheeting materials are preferably materials thatare dimensionally stable, durable, weatherable and readily formable intothe desired configuration. Examples of suitable materials includeacrylics, which generally have an index of refraction of about 1.5, suchas Plexiglas resin from Rohm and Haas; thermoset acrylates and epoxyacrylates, preferably radiation cured, polycarbonates, which have anindex of refraction of about 1.6; polyethylene-based ionomers (marketedunder the name ‘SURLYN’); polyesters; and cellulose acetate butyrates.Generally any optically transmissive material that is formable,typically under heat and pressure, can be used. Other suitable materialsfor forming retroreflective sheeting are disclosed in U.S. Pat. No.5,450,235 (Smith et al.). The sheeting can also include colorants, dyes,UV absorbers, or other additives as needed.

It is desirable in some circumstances to provide retroreflectivesheeting with a backing layer. A backing layer is particularly usefulfor retroreflective sheeting that reflects light according to theprinciples of total internal reflection. A suitable backing layer can bemade of any transparent or opaque material, including colored materials,that can be effectively engaged with the disclosed retroreflectivesheeting. Suitable backing materials include aluminum sheeting,galvanized steel, polymeric materials such as polymethyl methacrylates,polyesters, polyamids, polyvinyl fluorides, polycarbonates, polyvinylchlorides, polyurethanes, and a wide variety of laminates made fromthese and other materials.

The backing layer or sheet can be sealed in a grid pattern or any otherconfiguration suitable to the reflecting elements. Sealing can beaffected by use of a number of methods including ultrasonic welding,adhesives, or by heat sealing at discrete locations on the arrays ofreflecting elements (see, e.g. U.S. Pat. No. 3,924,928). Sealing isdesirable to inhibit the entry of contaminants such as soil and/ormoisture and to preserve air spaces adjacent the reflecting surfaces ofthe cube corner elements.

If added strength or toughness is required in the composite, backingsheets of polycarbonate, polybutryate or fiber-reinforced plastic can beused. Depending upon the degree of flexibility of the resultingretroreflective material, the material can be rolled or cut into stripsor other suitable designs. The retroreflective material can also bebacked with an adhesive and a release sheet to render it useful forapplication to any substrate without the added step of applying anadhesive or using other fastening means.

GLOSSARY OF SELECTED TERMS

-   An “array of neighboring cube corner elements” means a given cube    corner element together with all adjacent cube corner elements    bordering it.-   “Compound face” means a face composed of at least two    distinguishable faces (referred to as “constituent faces”) that are    proximate each other. The constituent faces are substantially    aligned with one another, but they can be offset translationally    and/or rotationally with respect to each other by relatively small    amounts (less than about 10 degrees of arc, and preferably less than    about 1 degree of arc) to achieve desired optical effects as    described herein.-   “Compound substrate” means a substrate formed from a machined    substrate having a structured surface and a replicated substrate    (collectively referred to as “layers”) bonded along at least a    portion of the interface with the machined substrate. One or more of    the layers of the compound substrate may be discontinuous.-   “Cube corner cavity” means a cavity bounded at least in part by    three faces arranged as a cube corner element.-   “Cube corner element” means a set of three faces that cooperate to    retroreflect light or to otherwise direct light to a desired    location. Some or all of the three faces can be compound faces.    “Cube corner element” also includes a set of three faces that itself    does not retroreflect light or otherwise direct light to a desired    location, but that if copied (in either a positive or negative    sense) in a suitable substrate forms a set of three faces that does    retroreflect light or otherwise direct light to a desired location.-   “Cube corner pyramid” means a mass of material having at least three    side faces arranged as a cube corner element.-   “Cube height” means, with respect to a cube corner element formed on    or formable on a substrate, the maximum separation along an axis    perpendicular to the substrate between portions of the cube corner    element.-   “Dihedral edge” of a cube corner element is an edge of one of the    three faces of the cube corner element that adjoins one of the two    other faces of the same cube corner element. Note that any    particular edge on a structured surface may or may not be a dihedral    edge, depending upon which cube corner element is being considered.-   “Direct machining” refers to forming in the plane of a substrate one    or more groove side surfaces typically by drawing a cutting tool    along an axis substantially parallel to the plane of the substrate.-   “Face” means a substantially smooth surface.-   “Geometric structure” means a protrusion or cavity having a    plurality of faces.-   “Groove” means a cavity elongated along a groove axis and bounded at    least in part by two opposed groove side surfaces.-   “Groove side surface” means a surface or series of surfaces capable    of being formed by drawing one or more cutting tools across a    substrate in a substantially continuous linear motion. Such motion    includes fly-cutting techniques where the cutting tool has a rotary    motion as it advances along a substantially linear path.-   “Nondihedral edge” of a cube corner element is an edge of one of the    three faces of the cube corner element that is not a dihedral edge    of such cube corner element. Note that any particular edge on a    structured surface may or may not be a nondihedral edge, depending    upon which cube corner element is being considered.-   “PG cube corner element” stands for “preferred geometry” cube corner    element, and is defined in the context of a structured surface of    cube corner elements that extends along a reference plane. For the    purposes of this application, a PG cube corner element means a cube    corner element that has at least one nondihedral edge that: (1) is    nonparallel to the reference plane; and (2) is substantially    parallel to an adjacent nondihedral edge of a neighboring cube    corner element. A cube corner element whose three reflective faces    are all rectangles (inclusive of squares) is one example of a PG    cube corner element.-   “Protrusion” has its broad ordinary meaning, and can comprise a    pyramid.-   “Pyramid” means a protrusion having three or more side faces that    meet at a vertex, and can include a frustum.-   “Reference plane” means a plane or other surface that approximates a    plane in the vicinity of a group of adjacent cube corner elements or    other geometric structures, the cube corner elements or geometric    structures being disposed along the plane.-   “Retroreflective” means having the characteristic that obliquely    incident incoming light is reflected in a direction antiparallel to    the incident direction, or nearly so, such that an observer at or    near the source of light can detect the reflected light.-   “Structured” when used in connection with a surface means a surface    that has a plurality of distinct faces arranged at various    orientations.-   “Symmetry axis” when used in connection with a cube corner element    refers to the vector that originates at the cube corner apex and    forms an equal acute angle with the three faces of the cube corner    element. It is also sometimes referred to as the optical axis of the    cube corner element.-   “Transition line” means a line or other elongated feature that    separates constituent faces of a compound face.-   “Waste pieces” means portions of the compound substrate that are    discarded using the present fabrication methods.

All patents and patent applications referred to herein are incorporatedby reference. Although the present invention has been described withreference to preferred embodiments, workers skilled in the art willrecognize that changes can be made in form and detail without departingfrom the spirit and scope of the invention.

What is claimed is:
 1. A compound substrate, comprising: a replicatedsubstrate having a structured surface; a plurality of machined substratepieces embedded in portions of the structured surface; and a pluralityof pg cube corner elements that each form a cube corner pyramid having amachined substrate piece in a portion of the structured surface and thateach have at least one compound face including a replicated substrateface and a machined substrate face.
 2. The substrate of claim 1, whereinthe plurality of cube corner elements each have a cube height of nogreater than about 1 mm and the replicated substrate face and machinedsubstrate face are disposed on opposite sides of a transition line thatis nonparallel to a dihedral edge of the cube corner element.
 3. Thesubstrate of claim 1, wherein the replicated substrate face and machinedsubstrate face are disposed on opposite sides of a transition line,wherein substantially all transition lines are parallel to a referenceplane.
 4. The substrate of claim 1, wherein the cube corner element hasan outline in plan view selected from the group of shapes consisting ofa hexagon and a quadrilateral.
 5. A compound substrate, comprising: areplicated substrate and a machined substrate, the replicated substratehaving a structured surface and a plurality of discrete pieces of themachined substrate in the structured surface such that at least threesides of each discrete piece of machined substrate are physicallyadjacent to the replicated substrate; each of the replicated andmachined substrates having an exposed surface that defines a compoundface, wherein the compound substrate is part of a pg cube cornerelement.
 6. The compound substrate of claim 5, wherein the structuredsurface of the replicated substrate includes cavities and the discretepieces of the machined substrate comprise a plurality of pyramids thatare adjacent to the cavities.
 7. The compound substrate of claim 6,wherein the pyramids and cavities form pg cube corner elements that haveassociated therewith a symmetrical entrance angularity.
 8. An articlemade by at least one replication from the substrate of claim
 5. 9. Acompound substrate, comprising: a structured surface including areplicated substrate portion and a machined substrate portion in thereplicated substrate portion, the compound substrate further comprisingat least one compound face including a substantially planar surfacehaving a first face portion on the machined substrate portion of thecompound substrate and a second face portion on the replicated substrateportion of the compound substrate, the first and second face portionsbeing on opposite sides of a transition line and cooperating to form apg cube corner element.
 10. A pg cube corner article made by at leastone replication from the substrate of claim 5.